chris invests $15,000 in a retirement account with an annual interest of 3.4%. find the final amount of the investment after 27 years of interest is compounded quarterly. round the answer to the nearest cent.
To find the final amount of the investment after 27 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years the money is invested for
Given:
P = $15,000
r = 3.4% = 0.034
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = 15000(1 + 0.034/4)^(4*27)
A = 15000(1 + 0.0085)^(108)
A = 15000(1.0085)^(108)
Calculating the value inside the parentheses:
(1.0085)^108 ≈ 3.17238
Multiplying by the principal amount:
A ≈ 15000 * 3.17238
A ≈ $47,886.99
Rounding the answer to the nearest cent:
A ≈ $47,886.99
The final amount of the investment after 27 years of interest is compounded quarterly is approximately $47,886.99.
wrong
Apologies for the mistake. Let's recalculate the answer correctly:
We will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years the money is invested for
Given:
P = $15,000
r = 3.4% = 0.034
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = 15000(1 + 0.034/4)^(4*27)
A = 15000(1 + 0.0085)^(108)
A = 15000(1.0085)^(108)
Calculating the value inside the parentheses:
(1.0085)^108 ≈ 1.346853
Multiplying by the principal amount:
A ≈ 15000 * 1.346853
A ≈ $20,202.80
Rounding the answer to the nearest cent:
A ≈ $20,202.80
The final amount of the investment after 27 years of interest is compounded quarterly is approximately $20,202.80.
find the final amount of a $15,000 investment with an annual interest rate of 3.4% after 27 years if interest is compounded quarterly. round to the nearest cent.
To find the final amount of the investment after 27 years with quarterly compounding, we need to use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years the money is invested for
Given:
P = $15,000
r = 3.4% = 0.034
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = 15000(1 + 0.034/4)^(4*27)
A = 15000(1 + 0.0085)^(108)
A = 15000(1.0085)^(108)
Calculating the value inside the parentheses:
(1.0085)^108 ≈ 3.05457
Multiplying by the principal amount:
A ≈ 15000 * 3.05457
A ≈ $45,818.55
Rounding the answer to the nearest cent:
A ≈ $45,818.55
The final amount of the investment after 27 years with quarterly compounding is approximately $45,818.55.